What is 1/8 plus 9/13? (Answer: 85/104)

Exact Answer

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Problem: What is 1/8 plus 9/13?
Formula / Expression: 1/8 + 9/13
Final Answer: 85/104
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 8 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 13 = 104.
Working: LCD(8, 13) = 104

Step 2: Convert to Equivalent Fractions with Common Denominator 104
Multiply the numerator and denominator of 1/8 by 13, and multiply the numerator and denominator of 9/13 by 8 so both fractions share the common base 104.
Working: 1 × 13/8 × 13 = 13/104 and 9 × 8/13 × 8 = 72/104

Step 3: Add the Numerators
Now add the numerators (13 + 72 = 85) and keep the common denominator 104 unchanged.
Working: 13 + 72/104 = 85/104

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 85 and 104 is 1, confirming that 85/104 cannot be reduced further—it is already in its simplest irreducible form.
Working: 85/104

Step 5: Decimal & Percentage Representation
Dividing the numerator 85 by denominator 104 produces a repeating decimal (approximately 0.817308, or 81.7308%).
Working: 85 ÷ 104 = 0.817308 (81.7308%)

Key Values:
- Simplified Fraction: 85/104
- Mixed Number Form: 85/104
- Decimal Value: 0.817308
- Percentage: 81.7308%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-8-plus-9-13/
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1/8 + 9/13 = 85/104

Simplified Fraction

85/104

Mixed Number

Proper (85/104)

Decimal Value

0.817308

Percentage

81.7308%

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Step-by-Step Solution: 1/8 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 8 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 13 = 104.

LCD(8, 13) = 104

Step 2

Convert to Equivalent Fractions with Common Denominator 104

Multiply the numerator and denominator of 1/8 by 13, and multiply the numerator and denominator of 9/13 by 8 so both fractions share the common base 104.

1 × 13/8 × 13 = 13/104 and 9 × 8/13 × 8 = 72/104

Step 3

Add the Numerators

Now add the numerators (13 + 72 = 85) and keep the common denominator 104 unchanged.

13 + 72/104 = 85/104

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 85 and 104 is 1, confirming that 85/104 cannot be reduced further—it is already in its simplest irreducible form.

85/104

Step 5

Decimal & Percentage Representation

Dividing the numerator 85 by denominator 104 produces a repeating decimal (approximately 0.817308, or 81.7308%).

85 ÷ 104 = 0.817308 (81.7308%)

Visual Representation

The diagram below illustrates 1/8 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`85/104`
Mixed Number Form	`85/104`
Decimal Form	`0.817308`
Percentage	`81.7308%`

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Frequently Asked Questions

What is 1/8 plus 9/13 as a fraction?

1/8 + 9/13 in simplest fraction form is 85/104.

What is 1/8 plus 9/13 as a decimal?

1/8 + 9/13 converted to a decimal is 0.817308.

What is 1/8 plus 9/13 as a percentage?

1/8 + 9/13 expressed as a percentage is 81.7308%.

Does 1/8 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.817308...) because the denominator contains prime factors other than 2 and 5.